Is it a good idea to pay for an deep learning course?
It doesn't seem expensive at $399* (although the asterix needs to be taken into consideration.)

If you're interested in this subject, this may be a decent course, however it is certainly not an accredited institution, thus any "degree" you get from this course will be meaningless in an academic sense.  On the other hand, a certificate shows that you've committed resources toward training.   

My high level take on this is that the "Foundation" is looking to capitalize on the recent publicity for Deep Learning, per the AlphaGo milestones.

One thing I can tell you for certain is that this field requires advanced mathematics from a research perspective, and people who work in that area spend years training to gain the requisite skills.  

The requirements for this class seem to be restricted to "Python knowledge" with no mention of mathematics, which raises some alarm bells, although it's worth mentioning that once solutions/applications arise, they can be applied to varying degrees without having to understand the mathematics. [See mindcrime's comment]